Rodgers was brought in to replace Coppell who stepped following a six-year stint during which he guided the club into the Premier League.
The former Crystal Palace, Brighton and Brentford manager has not thrown his hat into the ring and has not heard from his former employers.
Coppell returned to the Madejski Stadium to work for the media at the weekend as Reading drew 1-1 with Liverpool in the FA Cup third round.
But he does not anticipate being back in Berkshire on a regular basis.
Coppell said: "I went back for the first time to help with commentary for the Liverpool match in the FA Cup and no-one said anything to me.
"If they wanted me to come back they would have been in touch by now."